Fast boulder fracturing by thermal fatigue detected on stony asteroids

Spacecraft observations revealed that rocks on carbonaceous asteroids, which constitute the most numerous class by composition, can develop millimeter-to-meter-scale fractures due to thermal stresses. However, signatures of this process on the second-most populous group of asteroids, the S-complex, have been poorly constrained. Here, we report observations of boulders’ fractures on Dimorphos, which is the moonlet of the S-complex asteroid (65803) Didymos, the target of NASA’s Double Asteroid Redirection Test (DART) planetary defense mission. We show that the size-frequency distribution and orientation of the mapped fractures are consistent with formation through thermal fatigue. The fractures’ preferential orientation supports that these have originated in situ on Dimorphos boulders and not on Didymos boulders later transferred to Dimorphos. Based on our model of the fracture propagation, we propose that thermal fatigue on rocks exposed on the surface of S-type asteroids can form shallow, horizontally propagating fractures in much shorter timescales (100 kyr) than in the direction normal to the boulder surface (order of Myrs). The presence of boulder fields affected by thermal fracturing on near-Earth asteroid surfaces may contribute to an enhancement in the ejected mass and momentum from kinetic impactors when deflecting asteroids.

. Fracture length and hosting boulder diameter.We report the diameter (in meters) of each boulder hosting fractures, which is defined as the value of each ellipse's major axis fitted to each boulder, along with the number of mapped fractures.In addition, the range of both the length (in meters) and the ratio between the length of fractures and the hosting boulder dimension are reported.Such findings reveal that all fractures are smaller than the dimension of the hosting boulder.The gray rows represent the three boulders that have been thermophysically modeled.
Supplementary Figure 1.The three boulders where the thermophysical modeling has been applied: Atabaque Saxum (center, 6.62 m across and characterized by 6 cracks), a boulder with 1 crack (right, 5.29 m across), and a boulder with 2 cracks (left, 3.51 m in diameter).

Supplementary Figure 2.
The different illumination conditions used to understand how different lighting may play a role when identifying crack orientations.We decided to choose a boulder of Bennu because this one is affected by lineaments oriented in all directions.Moreover, its digital terrain model (DTM) has been produced by the OSIRIS-REX Laser Altimeter (Daly et al., 2017) with a 5 cm ground sampling distance.

Statistical analysis on the validity of fractures' orientation
We here report the analyses we have accomplished to strengthen the validity of our findings (preferred orientation of boulder's fractures).In particular, we investigate: 1) the probability that the observed azimuthal distribution arose by chance from a uniform Distribution, i.e. from randomly oriented fractures; 2) the sampling bias effect, implying that fractures with azimuth similar to the sunlight direction are less likely to be identified, and thus are not present from the dataset.
The observed azimuthal distribution coming from the fractures analysis performed in this work, coupled with a histogram representation is reported in Supplementary Figure 3.The resulting azimuth We investigate how likely it is to generate such a distribution as function of angular values by chance with statistical properties (mean and std) similar to our dataset.A clean null hypothesis for this study would result in a purely random orientation of fractures (with a process that could produce such a uniform distribution).If this hypothesis is verified, then any clustering in our data would arise by chance.We can establish a null hypothesis when the observed distribution arises from the sampling of a uniform distribution.To reject the null hypothesis, we need to demonstrate that our distribution, or one that is very similar to ours, cannot be generated by chance.Hence, we sample multiple times a random uniform distribution with the same sample size of the collected data.
To generate a uniform distribution, we first produce an example with the same number of samples as in our dataset, using a uniform distribution from 0° to 180°.The first plot of Supplementary Figure 4 shows our observed distribution as a reference.Then, we can repeat this sampling for a large number of cases (100000)some of which are shown below (Supplementary Figure 4) --and demonstrate that the likelihood to produce a standard deviation similar to the one we derived is small, i.e. near 0.129 %.This is of course limited from a statistical point of view, but it provides the indication that is quite unlikely that our dataset arises by chance from a uniform distribution (this can be defined with > 99 % confidence).
Supplementary Figure 4: Original dataset (in red) as a reference and some examples of generated uniform distributions.
Afterwards, we can make a simplified model of the expected effect of the lighting bias.The idea is that for fractures with the same azimuth of the Sunlight direction, the detection is impossible or at least very difficult.
To model this condition, we can start with a uniform distribution, where fractures with an azimuthal orientation similar to the one of the incoming light are more likely to remain undetectable, hence are not inside the final dataset.We report below an example that should clarify the issue, even if we are aware that such analysis is quite limited from a statistical perspective, but still quite illustrative.